The city Department of Education was fooled into paying out at least $1.5 million over two years to companies that lied about providing bilingual or special-education services to students, authorities said yesterday.

This was done in part by forging signatures on documents and falsifying the names of students serviced — including three who weren’t even attending the city’s public-school system at the time.

Federal officials arrested 35-year-old Nelson Ruiz, a co-owner of the five companies involved, and charged him with a slew of fraud charges and identity theft.

They said they were still seeking his partner, 41-year-old William Cruz, who is also known as Bill Chacon.

Their companies, which included Deaf & Hard of Hearing, Interpreting Spanish and Perfect Link Interpreting Services, had billing addresses with no offices and with no significant income apart from the city’s payments.

They allegedly charged at least $200,000 for special-education services in recent years for a single student who had left the school system in 2009.

Authorities said they couldn’t find a single legitimate bill the companies filed with the Department of Education since 2010.